This section illustrated the design of optimal spectrum-analysis
windows made using linear-programming (linprog in matlab) or
Remez multiple exchange algorithms (firpm in Matlab). After
formulating the Chebyshev window as a linear programming problem, we
found we could impose a monotonicity constraint on its shape in the
time domain, or various derivative constraints. In Chapter 4,
we will look at methods for FIR filter design, including the
window method (§4.5) which designs FIR filters as a
windowed ideal impulse response. The formulation introduced in this
section can be used to design such windows, and it can be used to
design optimal FIR filters. In such cases, the impulse response is
designed directly (as the window was here) to minimize an error
criterion subject to various equality and inequality constraints, as
discussed above for window design.4.16